e. Explain what a “particle in a box” is. It is a model that can be used to solve the Schrodinger equation. It is used to describe a particle that is free to move within a box. The box is confined because of the areas outside are infinite potentials. The particle is not allowed to be in the areas of infinite potential.
2. Answer the following questions. a. Describe the experimental results that led to quantum mechanics. The experiment that led to quantum mechanics is Schrödinger’s cat. The experiment was to put a cat in a box for an hour. The cat could be alive, or it could be dead, but that would be unknown until the box is open. So, the cat is equally alive and dead while the box is closed. This related to a particle having a wavelength. For something to have a wavelength it must occupy multiple positions at the same time. The wavelength of an object limited to a small space cannot be perfectly defined so it exists in multiple different wavelengths at the same time. b. Describe how to get the measured value (e.g. temperature or momentum) from a wavefunction. To get an expect or average value of temperature we integrate the complex conjugate of wavefunction, the temperature operator and wavefunction over space. c. Explain what atomic units are. SI units are used to describe things that we can see and bigger. An atom, nucleus, and electrons are so much smaller. They need to have their own units. To get atomic units from SI units normalize all the units so that everything is equals to 1. d. Explain why an electron around a proton nucleus doesn’t collapse into the nucleus. An electron in an atom spreads out according to its energy. The states with more energy are more spread out. All electron states overlap with the nucleus. Electrons are partially in the nucleus.
- Summer '20